First, it is probably wise to define the "Free French". This consisted of regular army units, totaling around 300,000 in 1944 but what of the irregular "French Forces of the Interior" (FFI) as De Gaulle dubbed the Resistance? In August 1944, De Gaulle informed the CNR, the "head" body of the resistance that they were incorporated into the whole Free French structure. Their leader, Georges Bidault, agreed to join the government as Foreign Minister which emphasises his acceptance of this. From this, we can see the regular units and FFI as one of the same- both contributing to the war effort (My apologies if this becomes more of a "how useful was the Resistance?" answer).

The level of intelligence information provided for Overlord was unprecedented at the time and that was thanks to the efforts of the FFI coordinating with British SOE/OSS agents. This was recognised by both Allied and German forces alike well encapsulated by an operations officer in a SS Panzer Division:

"We were astounded by the accuracy with which our fortifications were marked in. Even the weapons, right down to the light machine gun and mortars, were listed. And we were disgusted our own intelligence had not been able to stop this. We found out later on that a Frenchman...had spied for years in the Orne sector appearing every day in his greengrocer's van on the coastal road. We could clearly see in this map the result of his activities and that of other spies also".

There were of course some ommissions made by the FFI when reporting to the Allies but the network created since 1942 was an extraordinary success in terms of intelligence gathering which proved invaluable to the Allied offensive in June 1944.

In turn, we should also look at the impact the regular Free French had from the landings onwards. I will not go through the action of each individual French unit at Normandy, but this consisted of commando units, paratroopers, five airforce squadrons, and four naval vessels. Each fought valiantly and supported the overall effort though no sources argue any particular unit increased the chances of victory singlehandedly.

However, on the 16th August, 1944 General de Tassigny landed in Marseilles as part of Operation Dragoon to liberate the south of France. Although the operation was "supervised" by an American, the 1st French Army formed the bulk of the land forces and repeatedly picked up FFI units on their speedy push through the region. The combined effort of Allied armies in the north and the French in the South saw multiple German units going back and forth trying to defend both fronts allowing slight reprieve for Allied forces. The French 1st Armoured distinguished themselves by taking three Cuers, Brignoles and Salerne in rapid succession. Meanwhile, the skill of French commandos climbing into the fortresses of Toulon and Marseilles brought about a sudden surrender with a shock capture of 17,000 prisoners. There are some arguments that allowing Operation Dragoon to go ahead deprived Allied forces of supplies in Italy and Normandy making their advance slower (additionally shortages were already visible considering a shortage of landing craft meant Operation Dragoon could not commence on the same day as Overlord). However, the combined ferocity against German defences in Provence and the South placed the Allies a month ahead of schedule in late August, 1944.

I will not go on to list every successful French engagement ranging from Dragoon to their capture of Berchtesgaden, but their contribution to defeating the Germans during Operation Nordwind in January 1945 (described sometimes as the "lesser" Bulge) was a striking achievement. A robust German counter offensive (with superior armour and firepower) was stalled by de Tassigny who were determined to defend the city of Strasbourg, and not see a repeat of September 1870.

Overall thus success is what contributed hugely to France earning its seat in the peace process and their eventual place in the UNSC (despite initial snubs to attend Yalta and Dunbarton Oaks). The manpower contribution that the French made was a great benefit to the Allies as was their experience and drive to reclaim their homeland. With the FFI in tow, their intelligence contribution was invaluable as was their ability to hamper, hinder and delay German forces desperately moving across France to oppose the advancing Allied lines.

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Sources:

C Sowerine, France Since 1870 (London 2009)

A Roberts, The Storm of War (London 2010)

E Bauer, The History of World War II (London 1979)

I Matanle, World War II (London 1989)

Edit: grammar correction